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Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

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Abstract

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.

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References

  1. Tuchin, A.G., Quasi-Synchronous Orbits and Their Employment for the Approach of a Spacecraft to Phobos, Kosm. Issled., 2007, vol. 45, no. 2, pp. 144–149.

    Google Scholar 

  2. Henon, M., Numerical Exploration of the Restricted Problem. VI. Hill’s Case: Non-Periodic Orbits, Astron. Astrophys., 1970, vol. 24, no. 9, pp. 24–36.

    ADS  Google Scholar 

  3. Benest, D., Libration Effects for Retrograde Satellites in the Restricted Three-Body Problem, Cel. Mech., 1976, vol. 13, no. 2, pp. 203–215.

    Article  MATH  ADS  Google Scholar 

  4. Kogan, A.Yu., Far Satellite Orbits in the Restricted Circular Three-Body Problem, Kosm. Issled., 1988, vol. 26, no. 6, pp. 813–818.

    ADS  Google Scholar 

  5. Lidov, M.L. and Vashkov’yak, M.A., Quasi-Satellite Orbits for an Experiment Aimed at Refining the Gravitational Constant, Pis’ma Astron. Zh., 1994, vol. 20, no. 3, pp. 229–240.

    ADS  Google Scholar 

  6. Lidov, M.L. and Vashkov’yak, M.A., Quasi-Satellite Orbits in the Restricted Elliptical Three-Body Problem, Pis’ma Astron. Zh., 1994, vol. 20, no. 10, pp. 781–795.

    ADS  Google Scholar 

  7. Lidov. M.L., One Family of Three-Dimensional Periodic Orbits around the Moon and Planets, Dokl. Akad. Nauk SSSR, 1977, vol. 233, no. 6, pp. 1068–1071.

    ADS  Google Scholar 

  8. Lidov, M.L. and Rabinovich, V.Yu., A Study of Families of Three-Dimensional Periodic Orbits in the Three-Body Problem, Kosm. Issled., 1979, vol. 17, no. 3.

  9. Lidov. M.L, A Method of Constructing Families of Three-Dimensional Periodic Orbits in the Hill Problem, Kosm. Issled., 1982, vol. 20, no. 6, pp. 787–807.

    ADS  Google Scholar 

  10. Lidov, M.L. and Vashkov’yak, M.A., Perturbation Theory and Analysis of Evolution of Quasi-Satellite Orbits in a Restricted Three-Body Problem, Kosm. Issled., 1993, vol. 31, no. 2, pp. 75–99.

    ADS  Google Scholar 

  11. Akim, E.L., Zaslavskii, G.S., Morskoi, I.M., et al., Ballistics, Navigation, and Flight Control for a Spacecraft in the “Fobos-Grunt” Project, Izv. Akad. Nauk, Ser. Teor. Sist. Upr., 2002, no. 5.

  12. Shishov, V.A., Model of Phobos Motion and Method of Refining Parameters in the “Fobos-Grunt” Project, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2008, no. 10.

  13. Tuchin, A.G., Calculation of Quasi-Synchronous Orbits around Phobos for Solving the Task of Landing on Its Surface, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2008, no. 15.

  14. Akim, E.L., Popov, G.A., and Tuchin, A.G., Mechanics and Motion Control of a Space Vehicle in the Project of Relict Substance Delivery on Earth (The Project “Phobos-Grunt”), Proc. 16th IFAC Symposium on Automatic Control in Aerospace, Prenrints, Saint Petersburg, Russia, 2004, vol. 1.

    Google Scholar 

  15. Akim, E.L., Botkin, A.V., Stepaniants, V.A., et al., Orbit Selection, Navigation and Maneuvers before the Landing on the Phobos Surface for Phobos Sample Return Project, Proc. 17th Intern. Symposium on Space Flight Dynamics, 16–20 June, 2003, Moscow: Russia, vol. 1.

  16. Akim, E.L. Stepaniants, V.A., et al., Ballistics, Navigation and Motion Control of the SC on Stages of the Phobos Surface Approaching and Landing, Proc. 18th Intern. Symposium on Space Flight Dynamics, 11–15 October, 2004, Munich, Germany.

  17. Gradstein, I.S. and Ryzhik, I.M., Tablitsy integralov, summ, ryadov i proizvedenii (Tables of Integrals, Sums, Series, and Products), Moscow: Nauka, 1971.

    Google Scholar 

  18. Rastrigin, L.A., Sistemy ekstremal’nogo upravleniya (Systems of Extreme Control), Moscow: Nauka, 1974.

    Google Scholar 

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Original Russian Text © A.G. Tuchin, 2008, published in Kosmicheskie Issledovaniya, 2008, vol.46, No. 6, pp. 537–547.

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Tuchin, A.G. Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface. Cosmic Res 46, 506–516 (2008). https://doi.org/10.1134/S0010952508060051

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  • DOI: https://doi.org/10.1134/S0010952508060051

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